1. Field of the Invention
This invention relates to proportional-integral-derivative ("PID") controllers such as are used for the control of servo systems and the like, and in particular, to an apparatus for automatically setting the gain values associated with the proportional, integral, and derivative terms of the controller, that is, for "tuning" the controller.
2. Background Art
Feedback controllers, for example, feedback controllers used for controlling the positioning of a motor system, accept a position command indicating the desired position of the motor and a response or feedback signal indicating the actual position of the motor. From these signals, the controller produces a torque command or velocity command to the motor system, such torque or velocity command being calculated to bring the feedback signal into closer agreement with the position command.
In a simple controller, the feedback signal of position is subtracted from the position command to produce an error signal and the velocity command is proportional to the error signal. In more complex controllers, the torque or velocity command is a more complex function of the error signal.
The exact functional relationship between the error signal and the torque or velocity command critically affects the characteristics of the controlled motor system as reflected in criteria such as the "response time" of the system, i.e., how fast the motor moves to the desired position, "over shoot", i.e., how far the motor moves past the desired position before returning to the desired position, and the system "stability", whether the system is prone to oscillation under certain conditions. One aspect of system stability is the "damping ratio" of the system which generally describes how long the system oscillates in response to a step position command.
A variety of functional relationships between the error signal and the torque or velocity command can be obtained through the use of a PID controller which provides a generalized proportional-integral-differential function which is the sum of: (1) the error signal times a proportional gain factor ("P-gain"), (2) the integral of the error signal times an integral gain factor ("I-gain"), and (3) the derivative of the error signal times the derivative gain factor ("D-gain"). By adjusting the P, I and D-gain factors, a wide variety of transfer functions may be effected, which when combined with the physical transfer function of the servo system, produce the desired system response.
Selecting the proper P, I and D-gain factors to produce a desired system response is a subject of a considerable body of literature. If the transfer function of the physical system is well known and may be approximated by a linear system, the appropriate P, I and D gain factors may be calculated according to the desired response tradeoffs by a number of well known methods.
More typically, however, the precise transfer characteristics of the servo system are not well known and are determined by exciting the system with various inputs. With the increasing use of computers in control systems, a variety of computer controlled autotuning methods have been developed. In such computer controlled autotuning methods, the physical servo system is stimulated with a given input and the response characterized and used to adjust the PID gain factors.
Most of these autotune procedures employ a step or impulse function to measure the system response. These inputs have high frequency components and can excite instabilities and resonances that exist elsewhere in the system and which adversely affect the tuning results or cause the tuning process to fail. Certain of these autotuning procedures require the system to approach unstable behavior and then reduce the system gain by a preset amount. As the system approaches instability, high stress and damage to the system components may result and control of the system can be lost. Often such autotuning procedures must be restricted to low order, linear and low noise systems.